The diaphysis of the femur, i.e. the elongate part of this bone beginning at the lesser trochanter, has a relatively thick and strong cortex (cortical substance) and is therefore especially suitable for anchoring of a prosthesis shaft. Prostheses are known which exploit this fact in that their shaft extending into the diaphysis of the femur has a shaft cross-section which is adapted to the size of the medullary canal and has an approximately constant cross-section (U.S. Pat. No. 4,549,319, DE-A-2839092). It is true that there are also prostheses whose shaft cross-section tapers toward the end in the distal portion (EP-A-135755, U.S. Pat. No. 2,719,522, U.S. Pat. No. 3,067,740). However, these are either prostheses which are anchored with cement and whose cross-sectional difference from the medullary canal is therefore not important (Schneider: Die Totalprothese der Hüfte [The total hip prosthesis], page 120), or prostheses in which the shaft is intended to wedge itself in the medullary cavity by virtue of its wedge shape (Müller, loc. cit., page 214 et seq.). The latter have the disadvantage that the wedging leads to a high concentration of force at the wedge positions. However, a cementless force transmission is desired that covers a large surface area, but, based on previous experience, this requires individual adaptation of the prosthesis shaft to the shape of the medullary canal and, because of the very high costs involved, is normally not considered. They are also insufficiently secured-against twisting.